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Studies have been made on the phase transition phenomena of an oscillator network model based on a standard Hebb learning rule like the Hopfield model. The relative phase informations---the in-phase and anti-phase, can be embedded in the…
The Hopfield model is a paradigmatic model of neural networks that has been analyzed for many decades in the statistical physics, neuroscience, and machine learning communities. Inspired by the manifold hypothesis in machine learning, we…
Associative memory, a form of content-addressable memory, facilitates information storage and retrieval in many biological and physical systems. In statistical mechanics models, associative memory at equilibrium is represented through…
Networks of globally coupled, noise activated, bistable elements with connection time delays are considered. The dynamics of these systems is studied numerically using a Langevin description and analytically using (1) a Gaussian…
Neural dynamics of energy-based models are governed by energy minimization and the patterns stored in the network are retrieved when the system reaches equilibrium. However, when the system is driven by time-varying external input, the…
Most of animal and human behavior occurs on time scales much longer than the response times of individual neurons. In many cases, it is plausible that these long time scales emerge from the recurrent dynamics of electrical activity in…
The distinct timescales of synaptic plasticity and neural activity dynamics play an important role in the brain's learning and memory systems. Activity-dependent plasticity reshapes neural circuit architecture, determining spontaneous and…
We study a simple extended model of oscillator neural networks capable of storing sparsely coded phase patterns, in which information is encoded both in the mean firing rate and in the timing of spikes. Applying the methods of statistical…
Competition between synapses arises in some forms of correlation-based plasticity. Here we propose a game theory-inspired model of synaptic interactions whose dynamics is driven by competition between synapses in their weak and strong…
Slow adaption processes, like synaptic and intrinsic plasticity, abound in the brain and shape the landscape for the neural dynamics occurring on substantially faster timescales. At any given time the network is characterized by a set of…
We study both analytically and numerically the effects of including refractory periods in the Hopfield model for associative memory. These periods are introduced in the dynamics of the network as thresholds that depend on the state of the…
We discuss prototype formation in the Hopfield network. Typically, Hebbian learning with highly correlated states leads to degraded memory performance. We show this type of learning can lead to prototype formation, where unlearned states…
The study of neuronal interactions is currently at the center of several big collaborative neuroscience projects (including the Human Connectome Project, the Blue Brain Project, the Brainome, etc.) which attempt to obtain a detailed map of…
Learning or memory formation are associated with the strengthening of the synaptic connections between neurons according to a pattern reflected by the input. According to this theory a retained memory sequence is associated to a dynamic…
We investigate the role of the learning rate in a Kuramoto Model of coupled phase oscillators in which the coupling coefficients dynamically vary according to a Hebbian learning rule. According to the Hebbian theory, a synapse between two…
We obtain a result on the behavior of the solutions of a general nonautonomous Hopfield neural network model with delay, assuming some general bound for the product of consecutive terms in the sequence of neuron charging times and some…
We propose a new model based on the Ising model with the aim to study synaptic plasticity phenomena in neural networks. It is today well established in biology that the synapses or connections between certain types of neurons are…
Understanding the theoretical foundations of how memories are encoded and retrieved in neural populations is a central challenge in neuroscience. A popular theoretical scenario for modeling memory function is the attractor neural network…
It has been recently shown that a learning transition happens when a Hopfield Network stores examples generated as superpositions of random features, where new attractors corresponding to such features appear in the model. In this work we…
We study the dynamics of the contact-process, one of the simplest nonequilibrium stochastic processes, taking place on a scale-free network. We consider the network topology as annealed, i.e. all links are rewired at each microscopic time…